Problem: Divide the following complex numbers. $ \dfrac{12+4i}{-4i}$
Since we're dividing by a single term, we can simply divide each term in the numerator separately. $ \dfrac{12+4i}{-4i} = \dfrac{12}{-4i} + \dfrac{4i}{-4i}$ Factor out a $1/i$ $\dfrac{12}{-4i} + \dfrac{4i}{-4i} = \dfrac 1i \left( \dfrac{12}{-4} + \dfrac{4i}{-4} \right) = \dfrac 1i (-3-i)$ After simplification, $1/i$ is equal to $-i$, so we have: $\dfrac 1i (-3-i) = -i (-3-i) = 3i + 1i^2 = -1+3i$